In so many words, diddly-squat
What we have is archaeological evidence: monuments that remained unharmed, or were slowly buried underground, or in one awesome case ritually filled with stones, burnt, and covered with earth (Emain Macha in Navan Fort), and artifacts that were ritually deposited, generally in wetlands, or dropped and forgotten, or buried to be retrieved at a later date that never came. And a few bodies buried in bogs. It's easy to come up with explanations and draw conclusions based on modern interpretation and sheer blind guesswork. There's also the rather patronizing belief that all cultures go through roughly the same order of 'development' just at different rates, and so to figure out the ancient Irish you can just check out some primitive African tribe and see the same thing as what the Irish were doing 3000 years ago.
For example on the guesswork: ritual sites and religion. Passage graves like Newgrange could have only held a very small number of people within their chamber, and the rituals they performed would have been hidden from others. (This is assuming that passage graves were used for ritual, and goes along with the old archaeological standby -
if you don't get it, it must be religious!)
Another megalith type, the court tomb, had a fairly large forecourt capable of holding a good amount of people, and thus may point to a more open and less mysterious religion in the northwest of Ireland.
The enigmatic monument called a henge would, by these standards, indicate the most egalitarian religion of all: these are huge circular enclosures (around 180m in diameter!), they are clearly not for defense (they have a ditch
surrounded by a bank), and they are on low areas surrounded by and visible from hilltops: the entire community and then some would be privy to the rituals and tasks taking place in a henge.
What's very interesting is that henges occur in the Boyne Valley along with passage tombs - but they are from the Late Neolithic as opposed to the Early/Middle Neolithic passage tombs. I wonder what sort of societal upheaval occured to warrant this change? If there was any upheaval at all?
So you see Martin, you just opened a barrel of snakes. Spitting cobras, in fact. And we're gonna need more than St. Patrick to clear up this mess!
Go Billy, go!